1.

Factorise : `x^4+3x^2-28`

Answer» Here, a=3, b=-35,c=-52
`therefore axxc=-156`
Now, we take two factors of -156 whose sum is -35. Such factors are 4 and -39.
`therefore 3x^(4)-35x^(2)y^(2)-52y^(4)=3x^(4)-39x^(2)y^(2)+4x^(2)y^(2)-52y^(4)`
`=3x^(2)(x^(2)-13y^(2)+4y^(2)(x^(2)-13y^(2))`
`=(x^(2)-13y^(2))(3x^(2)+4y^(2))`
`[(x)^(2)-(sqrt(13)y)^(2)](3x^(2)+4y^(2))`
`=(x+sqrt(13)y)(x-sqrt(13)y)(3x^(2)+4y^(2))`


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